Fokker-Planck equation approach to vehicle statistics

Dirk Helbing; Martin Treiber

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Fokker-Planck equation approach to vehicle statistics

Dirk Helbing·Martin Treiber

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Abstract

This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint cond-mat/0301484). Despite the forwardly directed interactions and the additional driving terms in vehicle traffic, the steady-state velocity and distance distributions agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. Finally, this analytical result is confirmed by computer simulations.

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Dirk Helbing, Martin Treiber. 2003-07-09. Fokker-Planck equation approach to vehicle statistics. https://arxiv.org/abs/cond-mat/0307219

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